Transcript Food Webs Augmented With Additional Data: Structure and Dynamics

Food Webs Augmented With
Additional Data: Structure and
Dynamics
Daniel C. Reuman, Rockefeller University,
New York, U.S.A.
Joel E. Cohen, Rockefeller University and
Columbia University, New York, U.S.A.
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Networks and augmented
networks
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0.5
1.2
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Augmented food web: M,N-web
• Mi = average body mass of species i
• Ni = population density of species i
Species 1
(M1, N1)
Species 2
(M2, N2)
Species 4
(M4, N4)
Species 3
(M3, N3)
Species 5
(M5, N5)
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Examples of Real Augmented
Food Webs
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Tuesday Lake, Michigan
• Pelagic community only
• 1984: 25 phytoplankton, 22 zooplankton, 3
fish species
• Similar data for 1986
• Complete food web, average body mass (M)
and population density (N) for each species
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in each year
Tuesday Lake, 1984
Zooplankton
species
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Phytoplankton species
Fish species
Cohen Jonsson, Carpenter
PNAS, 2003
M = body mass (kg)
Circles = phytoplankton
Squares = zooplankton
Diamonds = fish
N = population density
(individuals/m3)
Jonsson, Cohen, Carpenter, Advances in
Ecological Research 2005
Tuesday Lake food web, body
mass & pop. density 1984
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Broadstone Stream, UK
http://www.biology.qmul.ac.uk/research/staff/hildrew/guy.htm
Data are available from other systems.
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Why add data to food webs?
• Traditional food web directed graphs have
sampling problems
– Martinez, Ecological Monographs, 1991
– Martinez et al., Ecology, 1999
• The food web model is unrealistic
– Predator-prey relationships differ
– Species with the same prey and same
predators differ
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Length of links
d1
log(M)
Predator
Define:
Length of link
= d1 + d2
d2
Prey
log(N)
Reuman and Cohen,
Journal of Animal
Ecology, 2004
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Frequency distribution of link length
Link lengths were normally distributed.
Lengths of all ordered pairs of species were
not normally distributed.
1984
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Niche and Cascade Models
• Models of food web directed graphs
• Given a list of species, they select links to
emulate the structure of real webs
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Failures of the Niche and Cascade
Models
• When combined with the M and N data of
Tuesday Lake, these models produced
webs with non-normal link length
distributions
• M,N structure of food webs interacts with
the network structure
• M,N structure illuminates network structure15
Better models
• To reproduce normal link length
distributions, assume:
– species are divided into 3 body-mass ranked
functional groups that can only eat lower
groups (e.g., plants, herbivores, carnivores)
– species do not eat other species that are too
much smaller (perceptual limit)
• Complete models of M,N-web structure
should be proposed and tested
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M,N-web structure varies
among communities of different
types
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Describing M,N structure with linear
models
For 162 local ecological communities,
we tested whether data satisfied the statistical
assumptions of standard linear models relating
log(M) and log(N).
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Ecosystem types
• The 162 communities were of nine types,
including:
– shores of a lake
– inside pitcher plants
– 7 types of soil community (farms, forest,
fields)
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Results
• Communities of some types were betterdescribed by linear models than communities
of other types
• M,N-web structure varies by ecosystem type
• The causes of this structural variation should
be studied
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Use of M,N-webs: biomass flux
along trophic links
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What is flux?
Predator
Given a food web and
a prey, predator pair …
How much biomass does
this predator eat of this prey
per unit time?
Prey
Want “flux” for all
prey-predator pairs
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What biomass flux occurred
along 269 trophic links in 1984,
241 trophic links in 1986?
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Fluxes are hard to measure
• Even for a single prey-predator pair
• Harder still to measure all fluxes
We want a model
Should estimate flux for all trophic links using
M,N-web data
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Example: Metabolic Action Model
If i = prey and j = predator,
Fij  (population production of i) 
(population consumptio n of j)
Pi  Ni M
3/ 4
i
Cj  N jM
3/ 4
j
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Why estimate flux?
Application: animal behavior
Predator
1/2
1/4
Prey 1
1/2
3/4
Prey 2
Null-model flux (kg/day)
Measured flux (kg/day)
Why the deviation
from expectation?
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Other possible applications
• Conservation
• Toxin concentrations going up the food
web
• Dynamics and stability of food webs
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Future
• Network models of food web structure that
include more information:
– An M distribution for each species
– Stoichiometric data for each species
– Distributions describing predation events
• Empirical biomass flux measurements to
compare to the model
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Thank you!
Questions?
References:
Reuman & Cohen, Trophic links’ length and slope
in the Tuesday Lake food web with species’
body mass and numerical abundance. 2004.
Journal of Animal Ecology 73, 852-866.
Reuman & Cohen, Estimating relative energy
fluxes using the food web, species abundance,
and body size. 2005. Advances in Ecological
Research 36,137-182.
Reuman & Cohen, Allometry of body size and
abundance in 166 food webs: tests of the
standard linear model. In prep.
Email: [email protected]
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Toy example of an augmented
network: friendship networks
40yrs
75yrs
1 hr/wk
28yrs
5 hrs/wk
0.25 hrs/wk
0.5 hrs/wk
50yrs
32yrs
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Toy example of an augmented
network: computer networks
1.4 GHz
One could include the
clock speed
4.0 GHz
2.2 GHz
1.7 GHz
3.2 GHz
One could also include
measures of
the network traffic
along each edge
1.2 GHz32
Broadstone Stream, UK
Predator mass > prey mass
Predator mass < prey mass
2
log10 mean individual body mass
(ug dry mass)
2
0
-2
-4
-6
-2
0
2
4
0
-2
-4
-6
-2
log10 pop. density (individuals /
0
2
4
m 2)
Woodward, Speirs, Hildrew, Advances in Ecological Research, 2005
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We also tested our 8 models with
other data, too
System
System
type
Number
webs
Avg. # taxa
Lake
Neuchatel
Riparian
8
162
Dutch soil
Soil
3
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Lake Neuchatel webs: Carolin Banasek-Richter and Marie-France Cattin Blandenier
Dutch soil webs: Christian Mulder
Preliminary indirect testing shows the Metabolic
Action Model is better than the other models
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for these systems, too.
Other M,N-webs data sets
• Tuesday Lake, Michigan, U.S.A.:
freshwater pelagic
• Broadstone Stream, England: freshwater
benthic
• Lake Neuchatel riparian zone, Switzerland
• Inquiline communities in pitcher plants,
Florida, U.S.A.
• Ythan Estuary, Scotland
• Caribbean marine food web
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• Various soil food webs
Why estimate flux?
Application: conservation
Pred. 1
Pred. 2
9/10
1/10
Threatened
species
1/10
Prey 1
1/10
A model can provide
guesses on:
1) which prey species
is most important for
conservation
2) which predator is
most destructive
8/10
Prey 2
Prey 3
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